This is an update to my posting at https://community.theme.co/forums/topic/update-notifications-not-showing-with-validated-license/#post-1155518
My service provider fixed it for me and told me that you should as well since it’s a core bug probably introduced with 4.3.3 or slightly earlier. Citing him, X theme update notifications will never show in multisite setups due to your custom method multisite_get_themes. The simplest fix would be to change
$themes[] = wp_get_theme ( $theme_dir );
to
$themes [ $theme_dir ] = wp_get_theme ( $theme_dir );
to correspond to the interface of wp_get_themes.